David Cameron called for sanctions against Burma to be eased after holding talks with opposition leader Aung San Suu Kyi.

Making a historic visit to the former British colony, the prime minister insisted that moves towards democratic reform should be rewarded.

He was standing alongside the Nobel Peace Prize laureate in the garden of the lakeside villa where she spent 15 years under house arrest.

The prime minister said: "I think it is right to suspend the sanctions that there are against Burma - to suspend them, not lift them."

Cameron continued: "[Burma] shouldn't be as poor as it is, it shouldn't have suffered under dictatorship for as long as it has and things don't have to be that way.

"There is the real prospect of change and I'm very much committed to working with you in trying to help make sure that your country makes those changes.

"I met with President Thein Sein today, and I think there are prospects for change in Burma, and I think it is right for the rest of the world to respond to those changes.

"Of course we must respond with caution, with care, we must always be sceptical and questioning, because we want to know those changes are irreversible, but … I think it is right to suspend the sanctions that there are against Burma - to suspend them, not lift them, and obviously not to include the arms embargo - because I do think it is important to send a signal that we want to help see the changes that can bring the growth of freedom, human rights and democracy in your country."

Aung San Suu Kyi said: "We still have a long way to go but we believe we can get there.

"I believe President Thein Sein is genuine about democratic reforms and I am very happy that Prime Minister Cameron thinks that the suspension of sanctions is the right way to respond to this. I support the … suspension, rather than the lifting, of sanctions, because this would be an acknowledgement of the role of the president and other reformers.

"This suspension would have taken place because of the steps taken by the president and other reformers, and it would also make it quite clear to those who are against reform that should they try to obstruct the way of the reformers, then sanctions could come back. So this would strengthen the hand of the reformers."

Aung San Suu Kyi paid tribute to the "help friends have given us over these last decades, especially Britain and other very close friends".

She added: "They have always understood our need for democracy, our desire to take our place in the world and the aspirations of our people.

"And we have always shared in the belief that what is necessary for Burma is an end to all ethnic conflict, respect for human rights - which would include the release of political prisoners - and the kind of development aid which will help to empower our people and take our country further towards the road to genuine democracy."

Cameron said he had invited Aung San Suu Kyi to visit Britain in June.

Had she attempted to leave Burma in previous years, she knew she would have been prevented from returning.

Cameron said: "For many years, Daw [Aunt] Aung San Suu Kyi was allowed, if she wanted to, to leave this country. You wrote that they would roll out the red carpet all the way to the aeroplane, and put you on to it, but never let you return ... I have invited Daw Suu today, to come to London in June, and to come to the United Kingdom in June, to also see your beloved Oxford in June, and that I think is a sign, if we're able to do this, of huge progress, that you will be able to leave your country, to return to your country, and to continue your work as a member of parliament."

Aung San Suu Kyi, who lived and studied in Britain during the 1960s and 1980s, responded: "Two years ago, I would have said: 'Thank you for the invitation, but sorry.' Now I am able to say: 'Well, perhaps.' And that's great progress."

The prime minister also paid tribute to the opposition leader, saying: "Everyone in the United Kingdom has been inspired by your struggle … What an inspiration it is to have followed your struggle, to have watched your incredible courage, and the light that you have shone to all those around the world who want to see freedom, democracy and greater human rights … It is an honour to stand by your side."

And he suggested that political reform would lead to economic prosperity in her country. "I can't speak for why the regime is acting in the way that it is, but I think it's clear when you look at Burma's neighbours you can see economies that are growing more quickly, you can see poverty that is being tackled more effectively, you're seeing in other countries … democracy going hand in hand with greater economic success and growth."

This is the last stop on Cameron's tour of Asia, in which he has visited five countries in five days: Japan, Indonesia, Malaysia, Singapore and Burma.